I've struggled with this issue a fair amount in Cranium Rats. A player could describe something that'd give a side a bonus, not necessarily their side, and that side would gain +1d in the conflict.

I limited it to +3d so we'd not spend hours on this, but I wanted it there so people would bring forth the environment and flesh out the scene (I have shoes and he doesn't, I am standing on the higher ground, etc.). The thing is, in CR you want to win, the arbitrer who gets to choose whether you'll get the bonus or not for a specific case is the only person who is not invested in that side winning/losing.

It came to be seen through Filip's help (who gamed the system as much as he could) that both he wouldn't suggest bonuses for a side he didn't want to win, and if one of his bonus-claims got rejected (for being not consistent with the scene, or not worthy of a bonus), he'd suggest another, and another, till he got to his +3.

Yes, this is also a Social Contract issue, but it intersects nicely. I think a solution I had was that each player could only provide one +1d. Perhaps each player could also only suggest one such bonus, and if it got rejected, that's it. Or something.